The disclosure is directed to a conveyor for conveying tissue logs to a saw. The conveyor may have multiple lanes for conveying the tissue logs toward the log saw. The lanes may have log advancement members operatively connected to drives that are controlled by a controller. The controller may be configured to control the drives and move the log advancement members to advance the logs toward the log saw for cutting independently of one another. In one embodiment as described in more detail below, the conveyor has 4 lanes, and the log saw has a saw head with a rotary blade mounted on a cutting arm that orbits relative to the lanes. The tissue log placed in each lane is able to move independently relative to the adjacent lane. For example, lane 1 may move independently from lane 2, lane 2 may move independently from lane 3, lane 3 may move independently from lane 4, and lane 4 may move independently from lane 1. Additionally, successive tissue logs placed in the same lane may be moved independently within the same lane.